Any ideas on how to get in contact with some schools?
How about your local Chinese Consulate office?
Have you heard of the Confucious Institute? One use to see a lot of ads there and they are world wide.
A couple of years ago my wife did a Chinese language course at Peking Uni through the auspices of the Confucious institute. They paid for the airfare, the lodgings within the uni grounds and an allowance which was the average monthly wage to cover any general spending.
WEll anyway after completeing the course she gets job offers emailed to her on occasional basis. We figure that what must happen, is prospective employers looking for foreign employees use the Confucious institute as a go between. So perhaps on a long shot you might also try your local Confucious Institute.
Be warned it can be quite frustrating though as most of the staff are local voluntary labour with the Senior person actually being a Chinese govt appointee. ( Well thats what its like in NZ)
While my wife was in Beijing uni iI visited her for a week and meet an American who was teaching the equivilent of English 101.for a contracted 1year period. I think he scored the job through his own uni. He said the job didnt pay that well and that he was actually dollar negative when comparing to what he would have been paid back home.
the Advice Cardsharp told you is certainly worth considering